Two late goals ensured that the Blades continue with the end of season momentum.
In the final ten minutes Jamie Murphy and Chris Porter were on target as the Blades came from behind to secure three more points.
The goals also ensured that the Blades stretched an unbeaten league run to six games.
Blades boss Clough again rotated his ranks, making four changes for the trip to the Potteries. Skipper Doyle, Freeman, Scougall and Baxter returned with Hill, McGinn, Davies and Porter dropping to the bench.
Freeman slotted in at left-back and Baxter and Scougall as advanced midfielders with Murphy kicking off as the lone striker on a slick surface, due to pre-match rain.
Vale forced the early chances and would have been disappointed not to have opened the scoring on five minutes. Dodds escaped his marker and after his shot came back off a post, he delivered a floated cross which beat Howard but Maguire headed over before Williamson arrived.
Doyle then had to cut out a cross from Williamson aimed for Myrie Williams before United's opening chance fell to Baxter, who cut in from the left but shot at goalkeeper Johnson on 12 minutes.
Ex Blades scholar Robertson headed wide a corner from Dodds soon after, whilst United's defence was stretched further when Collins limped off midway through the half - Hill was the replacement.
United stemmed the flow of Vale attacked in the early stages of the half and began to force the home side onto the back foot for spells but, a couple of long range free-kicks apart, Johnson was barely tested before the half-time whistle.
Early in the second half United were appealing for a penalty when Maguire appeared to be knocked off balance but with their first attack after the break, Port Vale opened the scoring. A pass from Yates appeared to take a deflection and wrong-foot Hill, allowing DODDS the space to fire beyond Howard's left-hand from close range.
United's response came from Scougall. The Scot had an effort blocked and then, on 58 minutes, he made a darting run and forced a low save from Johnson. A number of runs from Murphy, now operating on the left, also forced the home side back.
Howard saved from Knott but United's struggle to break through the Vale defence resulted in Porter replacing Baxter with around 20 minutes to go. Davies was Clough's last change a few minutes later, taking over from Coady.
As the game entered the final ten minutes, United levelled. Brayford found space on the right and his low delivery was perfect for MURPHY to delicately place into the far corner, beyond the reach of Johnson.
Despite Howard gathering Knott's cross at the second attempt, the equaliser gave United momentum in the closing minutes. Davies whipped in a number of corners and Murphy again went close, this time Johnson saved at his near post.
And the late pressure was rewarded with a goal in the 90th minute. This time it was Murphy who delivered the low cross from the right and PORTER was well-positioned to simply direct the ball into the unguarded net.
Four minutes of added time was announced soon after and, expectedly, Port Vale began to apply the pressure but the Blades were economical with the amount of bodies being pushed forward and held on to complete the league double over Micky Adams's side.
Port Vale: Johnson, Yates, Robertson, Dodds (Lloyd 76), Myrie Williams, Lines, Williamson (Hugill 76), Griffith (Shuker 87), Duffy, Knott.
Unused: Tomlin, Birchall, Smith.
Blades: Howard, Brayford, Maguire, Flynn, Doyle, Baxter (Porter 72), Collins (Hill 23), Coady (Davies 78), Scougall, Murphy, Freeman.
Unused: McGinn, Paynter, Long, Kennedy.